Can one equate Darcy with pride, and Elizabeth with prejudice?

I think only to a degree. In the end, both characters share in this theme but in different ways. Darcy's pride in his position in society leads him initially to scorn anyone outside of his own social circle. Pride and prejudice are intimately related in the novel. As critic A. Walton Litz comments, "in Pride and Prejudice one cannot equate Darcy with Pride, or Elizabeth with Prejudice; Darcy's pride of place is founded on social prejudice, while Elizabeth's initial prejudice against him is rooted in pride of her own quick perceptions." Darcy, having been brought up in such a way that he began to scorn all those outside his own social circle, must overcome his prejudice in order to see that Elizabeth would be a good wife for him and to win Elizabeth's heart. The overcoming of his prejudice is demonstrated when he treats the Gardiners with great civility. The Gardiners are a much lower class than Darcy, because Mr. Darcy is a lawyer and must practice a trade to earn a living, rather than living off of the interest of an estate as gentlemen do. From the beginning of the novel Elizabeth prides herself on her keen ability for perception. Yet this supposed ability is often lacking, as in Elizabeth's judgments of Darcy and Wickham.

Elizabeth's vanity clouds her judgment, making her prone to think ill of Darcy and to think well of Wickham. In the end, Elizabeth's rebukes of Darcy help him to realize his fault and to change accordingly, as demonstrated in his genuinely friendly treatment of the Gardiners, whom he previously would have scorned because of their low social class. Darcy's letter shows Elizabeth that her judgments were wrong and she realizes that they were based on vanity, not on reason.